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   "source": [
    "# 过拟合解决方法\n",
    "从上文已经知道，一般出现模型过拟合，我们可以通过以下手段去解决：\n",
    "+ 增加训练样本数量 => 从案例3.1可以看出通过增加训练集数量可以解决过拟合\n",
    "+ 降低模型复杂度 => 实际中一般是通过正则化来达到目的（可以简单就不要追求复杂）\n",
    "+ 增加正则化 => 主要有L1正则化和L2正则化，本质就是在损失函数中给模型的参数加一个惩罚，使的学到的参数尽可能简单\n",
    "+ 提前停止训练 => early stop，当训练样本下降到一定的误差，并且测试样本误差也下降到一定程度提前终止训练\n",
    "+ dropout => 训练的时候，随机的去掉一些网络中的隐藏层的节点\n",
    "\n",
    "本章，我们重点介绍实际生产环境中用的比较多的处理过拟合的方法，正则化和dropout。\n",
    "一般实际环境中，训练样本是及其宝贵的，需要我们想尽办法去获取，当训练样本足够多，过拟合就越不容易发生，所以这些手段只有训练样本比较稀缺的时候才需要用到。\n",
    "\n",
    "下面我们通过两个实际案例来说明正则化和dropout真的可以一定程度上解决过拟合的问题：\n",
    "\n",
    "1. 高维线性回归实验：通过正则化来解决过拟合\n",
    "2. fashion-mnist图像识别：通过dropout来解决过拟合问题\n",
    "\n",
    "## 1. 正则化解决过拟合\n",
    "### 1.1 定义模型结构\n",
    "为了更好的使用 pytorch lightling， 我们可以学习 pytorch lightling 为我们封装好的模型库 pytorch-lightning-bolts       \n",
    "安装方式：`pip install pytorch-lightning-bolts`       \n",
    "源码地址：https://github.com/PyTorchLightning/pytorch-lightning-bolts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import torch\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "from torch.nn import functional as F\n",
    "from torch.utils.data import DataLoader\n",
    "from torch.utils.data import TensorDataset\n",
    "import pytorch_lightning as pl\n",
    "import numpy as np\n",
    "\n",
    "class HighDimLRModel(pl.LightningModule):\n",
    "\n",
    "    def __init__(self, l1_strength=None, l2_strength=None):\n",
    "        super(HighDimLRModel, self).__init__()\n",
    "        self.l1_strength = l1_strength\n",
    "        self.l2_strength = l2_strength\n",
    "        self.n_train = 20  # 训练样本数量\n",
    "        self.n_test = 100  # 测试样本数量\n",
    "        self.n_dim = 200  # 样本特征数量\n",
    "        self.true_w = torch.ones(self.n_dim, 1) * 0.01  # 样本权重都是 0.01\n",
    "        self.true_b = 0.05  # 样本偏置\n",
    "        self.layer_1 = torch.nn.Linear(self.n_dim, 1)\n",
    "        self.epoch_valid_loss = []\n",
    "        self.epoch_train_loss = []\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.layer_1(x)\n",
    "\n",
    "    def training_step(self, batch, batch_idx):\n",
    "        # 必须提供：定于训练过程\n",
    "        x, y = batch\n",
    "\n",
    "        # flatten any input\n",
    "        x = x.view(x.size(0), -1)\n",
    "\n",
    "        y_hat = self(x)\n",
    "\n",
    "        loss = F.mse_loss(y_hat, y)\n",
    "\n",
    "        # L1 regularizer\n",
    "        if self.l1_strength is not None:\n",
    "            l1_reg = torch.tensor(0.)\n",
    "            for param in self.parameters():\n",
    "                l1_reg += torch.norm(param, 1)\n",
    "            loss += self.l1_strength * l1_reg\n",
    "\n",
    "        # L2 regularizer\n",
    "        if self.l2_strength is not None:\n",
    "            l2_reg = torch.tensor(0.)\n",
    "            for param in self.parameters():\n",
    "                l2_reg += torch.norm(param, 2)\n",
    "            loss += self.l2_strength * l2_reg\n",
    "\n",
    "        tensorboard_logs = {'train_mse_loss': loss}\n",
    "        progress_bar_metrics = tensorboard_logs\n",
    "        return {\n",
    "            'loss': loss,\n",
    "            'log': tensorboard_logs,\n",
    "            'progress_bar': progress_bar_metrics\n",
    "        }\n",
    "\n",
    "    def training_epoch_end(self, outputs):\n",
    "        # 结束一轮训练，自测一下\n",
    "        x, y = iter(self.train_loss_data).next()\n",
    "        y_hat = self.forward(x)\n",
    "        train_loss = F.mse_loss(y_hat, y)\n",
    "        self.epoch_train_loss.append(train_loss.item())\n",
    "        tensorboard_logs = {'train_loss': train_loss}\n",
    "        return {'loss': train_loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def validation_step(self, batch, batch_idx):\n",
    "        # 可选提供：定义测试过程\n",
    "        x, y = batch\n",
    "        y_hat = self.forward(x)\n",
    "        loss = F.mse_loss(y_hat, y)\n",
    "        tensorboard_logs = {'valid_loss': loss}\n",
    "        return {'val_loss': loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def validation_epoch_end(self, outputs):\n",
    "        # 可选提供：定义验证过程，验证集上效果，每轮都会验证\n",
    "        avg_val_loss = torch.stack([x['val_loss'] for x in outputs]).mean()\n",
    "        self.epoch_valid_loss.append(avg_val_loss.item())\n",
    "        tensorboard_logs = {'valid_loss': avg_val_loss}\n",
    "        return {'val_loss': avg_val_loss, 'log': tensorboard_logs, 'progress_bar': tensorboard_logs}\n",
    "\n",
    "    def configure_optimizers(self):\n",
    "        # 必须提供：定义优化器\n",
    "        # can return multiple optimizers and learning_rate schedulers\n",
    "        # (LBFGS it is automatically supported, no need for closure function)\n",
    "        return torch.optim.SGD(self.parameters(), lr=0.003)\n",
    "\n",
    "    def prepare_data(self):\n",
    "        # 准备数据集合，可选提供：lightling 默认会执行一次，防止重复执行\n",
    "        self.features = torch.randn((self.n_train + self.n_test, self.n_dim), dtype=torch.float)\n",
    "        mid_true_y = torch.matmul(self.features, self.true_w) + self.true_b\n",
    "        print('mid_true_y shape', mid_true_y.shape)\n",
    "        self.true_y = mid_true_y + torch.tensor(np.random.normal(0, 0.01, size=mid_true_y.size()), dtype=torch.float)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        # 必须提供：提供训练数据集\n",
    "        self.train_loss_data = DataLoader(TensorDataset(self.features[:20, :], self.true_y[:20]), batch_size=20, shuffle=False, num_workers=0)\n",
    "        return DataLoader(TensorDataset(self.features[:20, :], self.true_y[:20]), batch_size=1, shuffle=True, num_workers=0)\n",
    "\n",
    "    def val_dataloader(self):\n",
    "        # 可选提供：提供测试数据集\n",
    "        return DataLoader(TensorDataset(self.features[20:, :], self.true_y[20:]), batch_size=100, shuffle=False, num_workers=0)"
   ]
  },
  {
   "cell_type": "code",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "hdlr_model = HighDimLRModel()\n",
    "trainer = pl.Trainer(logger=False, max_epochs=10, num_sanity_val_steps=0, progress_bar_refresh_rate=0)\n",
    "trainer.fit(hdlr_model)\n",
    "\n",
    "import matplotlib.pyplot as plt  \n",
    "def plot_epoch_loss(train_loss_list, test_loss_list):\n",
    "    x_vals = list(range(len(train_loss_list)))\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('loss')\n",
    "    plt.plot(x_vals, train_loss_list, 'g--',label='train_loss')\n",
    "    plt.plot(x_vals, test_loss_list, 'r--',label='valid_loss')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "plot_epoch_loss(hdlr_model.epoch_train_loss, hdlr_model.epoch_valid_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "GPU available: False, used: False\nTPU available: False, using: 0 TPU cores\n\n  | Name    | Type   | Params\n-----------------------------------\n0 | layer_1 | Linear | 201   \nmid_true_y shape torch.Size([120, 1])\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 1080x360 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "hdlr_model2 = HighDimLRModel(l2_strength=3)\n",
    "trainer = pl.Trainer(logger=False, max_epochs=5, num_sanity_val_steps=0, progress_bar_refresh_rate=0, track_grad_norm=2)\n",
    "trainer.fit(hdlr_model2)\n",
    "plot_epoch_loss(hdlr_model2.epoch_train_loss, hdlr_model2.epoch_valid_loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到加入正则化之后，训练集和测试集合的损失都可以将到比较合理的位置。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 dropout 解决过拟合\n",
    "这次我们使用 fashion mnist 数据集合来说明用 dropout 可以有效解决过拟合问题。\n",
    "### 2.1 定义模型结构\n",
    "同样我们使用 pytorch lightling 快速定义模型结构。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import nessasary lib\n",
    "import os\n",
    "import torch\n",
    "import torchvision\n",
    "from torchvision import transforms\n",
    "from torch.nn import functional as F\n",
    "from torch.utils.data import DataLoader, random_split\n",
    "from torch.utils.data import TensorDataset\n",
    "import pytorch_lightning as pl\n",
    "from pytorch_lightning.metrics.functional import accuracy\n",
    "import numpy as np\n",
    "\n",
    "class DropOutModel(pl.LightningModule):\n",
    "\n",
    "    def __init__(self):\n",
    "        super(DropOutModel, self).__init__()\n",
    "        self.epoch_num = 0\n",
    "        # 定义模型结构，初始化参数\n",
    "        self.net = torch.nn.Sequential(\n",
    "            torch.nn.Linear(28*28, 256),\n",
    "            torch.nn.ReLU(),\n",
    "            torch.nn.Dropout(0.2),\n",
    "            torch.nn.Linear(256, 256), \n",
    "            torch.nn.ReLU(),\n",
    "            torch.nn.Dropout(0.5),\n",
    "            torch.nn.Linear(256, 10)\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        # 必须：定义模型\n",
    "        x = x.view(x.size(0), -1)\n",
    "        x = self.net(x)\n",
    "        return x\n",
    "\n",
    "    def training_step(self, batch, batch_nb):\n",
    "        # 必须提供：定义训练过程\n",
    "        x, y = batch\n",
    "        y_hat = self.forward(x)\n",
    "        # 模型损失函数在此处提供\n",
    "        loss = F.cross_entropy(y_hat, y)\n",
    "        tensorboard_logs = {'train_loss': loss}\n",
    "        return {'train_loss': loss, 'loss': loss, 'log': tensorboard_logs}\n",
    "    \n",
    "    def training_epoch_end(self, outputs):\n",
    "        # 可选提供：定义训练一个 epoch 结束后需要做的事情\n",
    "        train_avg_loss = torch.stack([x['train_loss'] for x in outputs]).mean()\n",
    "        tensorboard_logs = {'train_loss': train_avg_loss}\n",
    "        print('epoch_num={}: {}'.format(self.epoch_num + 1, tensorboard_logs))\n",
    "        self.epoch_num += 1\n",
    "        return {'train_loss': train_avg_loss, 'log': tensorboard_logs}\n",
    "\n",
    "    def test_step(self, batch, batch_nb):\n",
    "        # 可选提供：定义测试过程\n",
    "        x, y = batch\n",
    "        y_hat = self(x)\n",
    "        return {'test_loss': F.nll_loss(y_hat, y)}\n",
    "\n",
    "    def test_epoch_end(self, outputs):\n",
    "        # 可选提供：定义测试结束后需要做的事情\n",
    "        avg_loss = torch.stack([x['test_loss'] for x in outputs]).mean()\n",
    "        logs = {'test_loss': avg_loss}\n",
    "        return {'test_loss': avg_loss, 'log': logs, 'progress_bar': logs}\n",
    "\n",
    "    def validation_step(self, batch, batch_nb):\n",
    "        # 可选提供：定义验证过程\n",
    "        x, y = batch\n",
    "        y_hat = self.forward(x)\n",
    "        loss = F.cross_entropy(y_hat, y)\n",
    "        p_labels = torch.argmax(y_hat, dim=1)\n",
    "        acc = accuracy(p_labels, y)\n",
    "        return {'valid_loss': loss, 'valid_acc': acc}\n",
    "\n",
    "    def validation_epoch_end(self, outputs):\n",
    "        # 可选提供：定义一次验证结束后需要做的事情\n",
    "        valid_avg_loss = torch.stack([x['valid_loss'] for x in outputs]).mean()\n",
    "        valid_avg_acc = torch.stack([x['valid_acc'] for x in outputs]).mean()\n",
    "        logs = {'valid_loss': valid_avg_loss, 'valid_acc': valid_avg_acc}\n",
    "        print('epoch_num={}: {}'.format(self.epoch_num + 1, logs))\n",
    "        return {'valid_loss': valid_avg_loss, 'valid_acc': valid_avg_acc, 'log': logs, 'progress_bar': logs}\n",
    "\n",
    "    def configure_optimizers(self):\n",
    "        # 必须提供：定义优化器\n",
    "        return torch.optim.SGD(self.parameters(), lr=0.5)\n",
    "\n",
    "    def prepare_data(self):\n",
    "        # 可选提供：定义如何准备数据集\n",
    "        # 下载训练和测试数据集合，确保只下载一次\n",
    "        torchvision.datasets.FashionMNIST('../../datas', train=False, download=True)\n",
    "        mnist_data = torchvision.datasets.FashionMNIST('../../datas', train=True, download=True,\n",
    "            transform=transforms.Compose([\n",
    "                transforms.ToTensor(),\n",
    "                transforms.Normalize((0.1307,), (0.3081,))\n",
    "            ]))\n",
    "        self.train_set, self.val_set = random_split(mnist_data, [55000, 5000])\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        # 必须提供：提供训练数据集\n",
    "        \n",
    "        print(len(self.val_set))\n",
    "        return DataLoader(self.train_set, batch_size=128, shuffle=True, num_workers=4)\n",
    "\n",
    "    def val_dataloader(self):\n",
    "        # 必须提供：提供验证数据集\n",
    "        return DataLoader(self.val_set, batch_size=128, shuffle=True, num_workers=4)\n",
    "\n",
    "    def test_dataloader(self):\n",
    "        # 可选提供：提供测试数据集\n",
    "        mnist_test = torchvision.datasets.FashionMNIST('../../datas', train=False, download=False,\n",
    "            transform=transforms.Compose([\n",
    "                transforms.ToTensor(),\n",
    "                transforms.Normalize((0.1307,), (0.3081,))\n",
    "            ]))\n",
    "        return DataLoader(mnist_test, batch_size=128, shuffle=False, num_workers=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "GPU available: False, used: False\nTPU available: False, using: 0 TPU cores\n\n  | Name | Type       | Params\n------------------------------------\n0 | net  | Sequential | 269 K \n5000\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "55a2facc8cc34be2aa197bb96ef862c4"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Validating', layout=Layout(flex='2'), m…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "37d32de158f24308bdd908bd9af2bdd2"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch_num=1: {'valid_loss': tensor(0.5732), 'valid_acc': tensor(0.7953)}\nepoch_num=1: {'train_loss': tensor(0.9465)}\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Validating', layout=Layout(flex='2'), m…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "26f02017db7643138941d32080fdc76c"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch_num=2: {'valid_loss': tensor(0.5124), 'valid_acc': tensor(0.8010)}\nepoch_num=2: {'train_loss': tensor(0.6119)}\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Validating', layout=Layout(flex='2'), m…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "255253b7213e4d7bb1682b118e4353c5"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch_num=3: {'valid_loss': tensor(0.4889), 'valid_acc': tensor(0.8217)}\nepoch_num=3: {'train_loss': tensor(0.5337)}\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Validating', layout=Layout(flex='2'), m…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "98d08bcf70fa47fb856c6ac6e77b0d44"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch_num=4: {'valid_loss': tensor(0.4187), 'valid_acc': tensor(0.8482)}\nepoch_num=4: {'train_loss': tensor(0.4932)}\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Validating', layout=Layout(flex='2'), m…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "b31903c931904849a63397db76a47592"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "epoch_num=5: {'valid_loss': tensor(0.4405), 'valid_acc': tensor(0.8473)}\nepoch_num=5: {'train_loss': tensor(0.4537)}\n\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1"
     },
     "metadata": {},
     "execution_count": 56
    }
   ],
   "source": [
    "dropout_model = DropOutModel()\n",
    "\n",
    "# most basic trainer, uses good defaults (1 gpu)\n",
    "trainer = pl.Trainer(max_epochs=5, num_sanity_val_steps=0, progress_bar_refresh_rate=1)\n",
    "trainer.fit(dropout_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到，训练精度和验证测试集的精度稳步提升，验证数据集精确率达到了: 84.73%。"
   ]
  }
 ]
}